Question

state the excluded value for the rational equation.
\\(\frac{4}{2x - 1} = \frac{5}{3x + 2}\\)

select one:
\\(\bigcirc\\) a. \\(x = -\frac{1}{2}, \frac{2}{3}\\)
\\(\bigcirc\\) b. \\(x = \frac{1}{2}\\)
\\(\bigcirc\\) c. \\(x = -\frac{2}{3}, \frac{1}{2}\\)
\\(\bigcirc\\) d. \\(x = -\frac{2}{3}\\)

Explanation:

Step1: Set left denominator to 0

$2x - 1 = 0$

Step2: Solve for x (left denominator)

$2x=1 \implies x=\frac{1}{2}$

Step3: Set right denominator to 0

$3x + 2 = 0$

Step4: Solve for x (right denominator)

$3x=-2 \implies x=-\frac{2}{3}$

Answer:

C. $x = -\frac{2}{3}, \frac{1}{2}$